scholarly journals Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1430
Author(s):  
Fernando Barbero ◽  
Marc Basquens ◽  
Valle Varo ◽  
Eduardo J. S. Villaseñor
Keyword(s):  
General Relativity ◽  
Configuration Space ◽  
Equations Of Motion ◽  
Manifolds With Boundary ◽  
Test Bed ◽  
Hamiltonian Description ◽  
Gravitational Theories ◽  
The One ◽  
Direct Use ◽  
Singular Lagrangians

The Hamiltonian description of mechanical or field models defined by singular Lagrangians plays a central role in physics. A number of methods are known for this purpose, the most popular of them being the one developed by Dirac. Here, we discuss other approaches to this problem that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space. Owing to its interesting relation with general relativity we use a concrete example as a test bed: an extension of the Pontryagin and Husain–Kuchař actions to four dimensional manifolds with boundary.

FORMAL ANALOGIES BETWEEN GRAVITATION AND ELECTRODYNAMICS

2009 ◽  
Vol 24 (24) ◽  
pp. 4589-4605 ◽  
Author(s):  
E. GOULART ◽  
F. T. FALCIANO
Keyword(s):  
General Relativity ◽  
Equations Of Motion ◽  
Theoretical Framework ◽  
Gravitational Theories

We develop a theoretical framework that allows us to compare electromagnetism with gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as it is sometimes done in the literature. We construct the electromagnetic analogue to Riemann and Weyl tensors and develop the equations of motion for these objects. In particular, we are able to identify precisely how and in what conditions gravity can be mapped to electrodynamics. As a consequence, many of the geometrical tools of General Relativity can be applied to electromagnetism and vice versa. We hope our results would shed new light in the nature of electromagnetic and gravitational theories.

Elasticity in general relativity

1963 ◽  
Vol 272 (1348) ◽  
pp. 44-53 ◽  
Keyword(s):  
General Relativity ◽  
Elasticity Theory ◽  
Elastic Body ◽  
Equations Of Motion ◽  
Rigid Motion ◽  
Theory Of Elasticity ◽  
Body Motion ◽  
Einstein Tensor ◽  
Third Order ◽  
The One

This paper develops a new theory of elasticity in general relativity distinct from the one proposed by Synge (1959). In the new theory, stress is related to strain by a formula analogous to Hooke’s law, whereas Synge’s theory is formulated in terms of rates of change of stress and strain. Special features of the new theory are: (1) With any elastic body motion there is a uniquely associated rigid motion (in the Born sense), which plays a role analogous to that of the rigid body in the ordinary elasticity theory. (2) The 4-velocity of matter is an eigenvector of the Einstein tensor. (3) At each point of an elastic body there are at most 21 independent elastic coefficients. (4) The differential equations of motion of an elastic body are of the second order. (In Synge’s theory the corresponding equations are of the third order.) (5) As in Synge’s theory, shock waves travel with the same speeds as occur in ordinary elasticity theory. In the formulation of the new theory, consistent use is made of Lie derivatives.

scholarly journals Light field integration in SUGRA theories

2015 ◽  
Vol 30 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Diego Gallego
Keyword(s):  
Analytic Continuation ◽  
Configuration Space ◽  
Light Field ◽  
Equations Of Motion ◽  
Invariant Function ◽  
Field Configuration ◽  
Effective Theory ◽  
Gauge Symmetries ◽  
The One ◽  
Breaking Scale

We revisit the integration of fields in 𝒩 = 1 Supergravity with the requirement that the effective theory has a reliable two-derivative supersymmetric description. In particular, we study, in a supersymmetric manifest way, the situation where the fields that are mapped out have masses comparable to the Supersymmetry breaking scale and masses of the remaining fields. We find that as long as one stands in regions of the field configuration space where the analytic continuation to superspace of the F-flatness conditions be reliable equations of motion for the fields that are being mapped out, and provided their solutions are stable regardless the dynamics of the remaining fields, such a two-derivative description is a reliable truncation of the full effective theory. The study is mainly focused to models with two chiral sectors, H and L, described by a Kähler invariant function with schematic dependencies of the form [Formula: see text], which leads to a nearly decoupled theory that allows the previous requirements to be easily satisfied in a consistent way. Interestingly, enough for the matters of our study, this kind of models present a scenario that is as safe as the one presented in sequestered models. It is also possible to allow gauge symmetries as long as these appear also factorized in hidden and visible sectors. Then, the integration of the hidden vector superfields is compulsory and proceeds reliably through the D-flatness condition analytically continued to superspace.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

scholarly journals Non-Riemannian gravity actions from double field theory

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
A. D. Gallegos ◽  
U. Gürsoy ◽  
S. Verma ◽  
N. Zinnato
Keyword(s):  
Field Theory ◽  
Quantum Gravity ◽  
Condensed Matter ◽  
Equations Of Motion ◽  
Technical Note ◽  
Action Principle ◽  
Relativistic Symmetry ◽  
Gravitational Theories ◽  
Double Field Theory

Abstract Non-Riemannian gravitational theories suggest alternative avenues to understand properties of quantum gravity and provide a concrete setting to study condensed matter systems with non-relativistic symmetry. Derivation of an action principle for these theories generally proved challenging for various reasons. In this technical note, we employ the formulation of double field theory to construct actions for a variety of such theories. This formulation helps removing ambiguities in the corresponding equations of motion. In particular, we embed Torsional Newton-Cartan gravity, Carrollian gravity and String Newton-Cartan gravity in double field theory, derive their actions and compare with the previously obtained results in literature.

scholarly journals Gamma Astrometric Measurement Experiment: testing General Relativity with a small mission

2007 ◽  
Vol 3 (S248) ◽  
pp. 290-291 ◽  
Author(s):  
A. Vecchiato ◽  
M. G. Lattanzi ◽  
M. Gai ◽  
R. Morbidelli
Keyword(s):  
General Relativity ◽  
Solar Eclipse ◽  
Galactic Center ◽  
The Sun ◽  
Measurement Experiment ◽  
The One ◽  
First Time ◽  
Bending Of Light

AbstractGAME (Gamma Astrometric Measurement Experiment) is a concept for an experiment whose goal is to measure from space the γ parameter of the Parameterized Post-Newtonian formalism, by means of a satellite orbiting at 1 AU from the Sun and looking as close as possible to its limb. This technique resembles the one used during the solar eclipse of 1919, when Dyson, Eddington and collaborators measured for the first time the gravitational bending of light. Simple estimations suggest that, possibly within the budget of a small mission, one could reach the 10−6level of accuracy with ~106observations of relatively bright stars at about 2° apart from the Sun. Further simulations show that this result could be reached with only 20 days of measurements on stars ofV≤ 17 uniformly distributed. A quick look at real star densities suggests that this result could be greatly improved by observing particularly crowded regions near the galactic center.

scholarly journals The New Evolution for SIA Rotorcraft UAV Project

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Juntong Qi ◽  
Dalei Song ◽  
Lei Dai ◽  
Jianda Han ◽  
Yuechao Wang
Keyword(s):  
Control Method ◽  
Test Bed ◽  
Advanced Control ◽  
Autonomous Mode ◽  
Chinese Academy Of Sciences ◽  
Aerial Vehicle ◽  
Active Modeling ◽  
Rotorcraft Uav ◽  
The One ◽  
Academy Of Sciences

This paper describes recent research on the design, implement, and testing of a new small-scaled rotorcraft Unmanned Aerial Vehicle (RUAV) system—ServoHeli-40. A turbine-powered UAV weighted less than 15 kg was designed, and its major components were tested at the Shenyang Institute of Automation, Chinese Academy of Sciences in Shenyang, China. The aircraft was designed to reach a top speed of more than 20 mps, flying a distance of more than 10 kilometers, and it is going to be used as a test-bed for experimentally evaluating advanced control methodologies dedicated on improving the maneuverability, reliability, as well as autonomy of RUAV. Sensors and controller are all onboard. The full system has been tested successfully in the autonomous mode using the multichannel active modeling controller. The results show that in a real windy environment the rotorcraft UAV can follow the trajectory which was assigned by the ground control station exactly, and the new control method is obviously more effective than the one in the past year's research.

scholarly journals Astronomical tests of relativity: beyond parameterized post-Newtonian formalism (PPN), to testing fundamental principles

2009 ◽  
Vol 5 (S261) ◽  
pp. 56-61 ◽  
Author(s):  
Vladik Kreinovich
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Final Theory ◽  
Gravitational Theories ◽  
Cosmological Observations ◽  
Partial Analysis ◽  
Theory Of Gravitation ◽  
Improved Accuracy ◽  
Fundamental Physical ◽  
Relativistic Gravitation

AbstractBy the early 1970s, the improved accuracy of astrometric and time measurements enabled researchers not only to experimentally compare relativistic gravity with the Newtonian predictions, but also to compare different relativistic gravitational theories (e.g., the Brans-Dicke Scalar-Tensor Theory of Gravitation). For this comparison, Kip Thorne and others developed the Parameterized Post-Newtonian Formalism (PPN), and derived the dependence of different astronomically observable effects on the values of the corresponding parameters.Since then, all the observations have confirmed General Relativity. In other words, the question of which relativistic gravitation theory is in the best accordance with the experiments has been largely settled. This does not mean that General Relativity is the final theory of gravitation: it needs to be reconciled with quantum physics (into quantum gravity), it may also need to be reconciled with numerous surprising cosmological observations, etc. It is, therefore, reasonable to prepare an extended version of the PPN formalism, that will enable us to test possible quantum-related modifications of General Relativity.In particular, we need to include the possibility of violating fundamental principles that underlie the PPN formalism but that may be violated in quantum physics, such as scale-invariance, T-invariance, P-invariance, energy conservation, spatial isotropy violations, etc. In this paper, we present the first attempt to design the corresponding extended PPN formalism, with the (partial) analysis of the relation between the corresponding fundamental physical principles.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

The mechanics of general relativity

1959 ◽  
Vol 251 (1264) ◽  
pp. 55-65 ◽  
Keyword(s):  
General Relativity ◽  
General Theory ◽  
Equations Of Motion ◽  
Stress Singularity ◽  
Theory Of Relativity ◽  
General Theory Of Relativity

It is shown how to obtain, within the general theory of relativity, equations of motion for two oscillating masses at the ends of a spring of given law of force. The method of Einstein, Infeld & Hoffmann is used, and the force in the spring is represented by a stress singularity. The detailed calculations are taken to the Newtonian order.

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